Showing papers in "Journal of the Physical Society of Japan in 2005"

Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances

Abstract: We present a manifestly gauge-invariant description of Chern numbers associated with the Berry connection defined on a discretized Brillouin zone. It provides an efficient method of computing (spin) Hall conductances without specifying gauge-fixing conditions. We demonstrate that it correctly reproduces quantized Hall conductances even on a coarsely discretized Brillouin zone. A gauge-dependent integer-valued field, which plays a key role in the formulation, is evaluated in several gauges. An extension to the non-Abelian Berry connection is also given.

Theory of Electronic States and Transport in Carbon Nanotubes

Abstract: A brief review is given of electronic and transport properties of carbon nanotubes obtained mainly in a k · p scheme. The topics include a giant Aharonov–Bohm effect on the band gap and a Landau-level formation in magnetic fields, magnetic properties, interaction effects on the band structure, optical absorption spectra, and exciton effects. Transport properties are also discussed including absence of backward scattering except for scatterers with a potential range smaller than the lattice constant, its extension to multi-channel cases, a conductance quantization in the presence of short-range and strong scatterers such as lattice vacancies, and transport across junctions between nanotubes with different diameters. A continuum model for phonons in the long-wavelength limit and the resistivity determined by phonon scattering are reviewed as well.

Quantum Dynamics of System Strongly Coupled to Low-Temperature Colored Noise Bath: Reduced Hierarchy Equations Approach

Abstract: Reduced equations of motion for a two-level system strongly coupled to a harmonic oscillators bath are constructed by extending the hierarchy of equations introduced by Tanimura and Kubo [J. Phys. ...

A Drastic Change of the Fermi Surface at a Critical Pressure in CeRhIn5: dHvA Study under Pressure

Abstract: We carried out the de Haas–van Alphen (dHvA) experiment for an antiferromagnet CeRhIn 5 at high pressures up to 3 GPa. The cross-sectional areas of the Fermi surfaces due to main dHvA branches α i and β 2 at ambient pressure, which are well explained by two kinds of nearly cylindrical Fermi surfaces of a non-4 f reference compound LaRhIn 5 , are unchanged up to about 2.3 GPa, while the corresponding cyclotron masses m c * increase steeply above a pressure P * = 1.6 GPa where pressure-induced superconductivity sets in : m * c = 5.5 m 0 at ambient pressure, 20 m 0 at 1.6 GPa and 60 m 0 at 2.2 GPa for branch β 2 , for example. Above 2.4 GPa, new dHvA branches appear, which are in good agreement with the corresponding dHvA branches of a 4 f -itinerant heavy fermion superconductor CeCoIn 5 , indicating that the 4 f electron of CeRhIn 5 becomes itinerant and significantly contributes to the volume of the Fermi surface. The 4 f -electron character is thus changed from localized to itinerant at a critical pressur...

The Short Pulse Equation Is Integrable

Abstract: We prove that the Schafer–Wayne short pulse equation (SPE), which describes the propagation of ultrashort optical pulses in nonlinear media, is integrable. First, we discover a Lax pair of the SPE that is found to be of the Wadati–Konno–Ichikawa type. Second, we construct a chain of transformations that relates the SPE with the sine-Gordon equation.

Superconductivity in a New Pseudo-Binary Li2B(Pd1-xPtx)3 (x=0–1) Boride System

Abstract: Recently we have found superconductivity in a cubic antiperovskite-like compound Li 2 BPd 3 . A new pseudo-binary complete solid solution Li 2 B(Pd 1- x Pt x ) 3 , x =0–1 with similar structure has been synthesized and observation of superconductivity in the entire x -range is reported. Our results strongly suggest that superconductivity is of bulk type. Critical temperature T c is decreasing approximately linearly with amount ( x ) of Pt from 7.2–8 K for Li 2 BPd 3 to 2.2–2.8 K for Li 2 BPt 3 . From isothermal magnetization ( M – H ) measurements, lower critical fields H c1 (138 Oe/ x =0 , 38 Oe/ x =1 ), upper critical fields H c2 WHH (3.4 T/ x =0 , 1 T/ x =1 ), coherence length ξ(0) (9.8 nm/ x =0 , 17.9 nm/ x =1 ) and penetration depth λ(0) (190 nm/ x =0 , 364 nm x =1 ) were estimated and shown to follow approximately linear dependencies with x , either. Structure and superconducting similarities with MgCNi 3 , viewed as a bridge between low and high T c superconductors are increasing the expectations t...

Exotic Heavy-Fermion State in Filled Skutterudite SmOs4Sb12

Abstract: Specific heat and transport measurements have revealed an unconventional heavy-fermion (HF) state in SmOs 4 Sb 12 single crystals. The electronic specific-heat coefficient (γ=0.82 J/K 2 mol) and the coefficient ( A ) of the quadratic temperature dependence of electrical resistivity are largely enhanced, although the ratio A γ -2 is reduced from the Kadowaki–Woods ratio of HF materials. Both γ and A do not show any significant decrease in applied field in contrast with Ce-based HF compounds, suggesting an unconventional origin of the heavy quasiparticles. A weak ferromagnetic ordering sets in below ∼3 K, probably originating in the itinerant quasiparticles.

Novel Kondo Behaviors Realized in the Filled Skutterudite Structure

Abstract: Novel Kondo-like behaviors realized in the Pr-based filled skutterudites are reviewed based on the electronic transport properties, specific heat and de Haas–van Alphen (dHvA) experiments, along wi...

The ALPS Project: Open Source Software for Strongly Correlated Systems

Abstract: We present the ALPS (Algorithms and Libraries for Physics Simulations) project, an international open source software project to develop libraries and application programs for the simulation of strongly correlated quantum lattice models such as quantum magnets, lattice bosons, and strongly correlated fermion systems. Development is centered on common XML and binary data formats, on libraries to simplify and speed up code development, and on full-featured simulation programs. The programs enable non-experts to start carrying out numerical simulations by providing basic implementations of the important algorithms for quantum lattice models: classical and quantum Monte Carlo (QMC) using non-local updates, extended ensemble simulations, exact and full diagonalization (ED), as well as the density matrix renormalization group (DMRG). The software is available from our web server at http://alps.comp-phys.org/.

Double Beta Decays and Neutrino Masses

Abstract: Neutrino-less double beta decays (0νββ), which violate the lepton number conservation law by Δ L = 2, are of great interest for studying the fundamental properties of neutrinos beyond the standard ...

Possible Octupole Ordering in Phase II of SmRu4P12 Suggested from Elastic Constants

Abstract: We have studied the origin of the successive phase transitions in filled skutterudite SmRu 4 P 12 based on the results of elastic constant measurements. The temperature dependence of the elastic constants shows a sharp drop at the metal–insulator (M–I) transition of T MI = 16.5 K in a zero field. The successive transition at T N = 14 K is indistinct in a low field. The anomaly at T MI disappears with increasing field. A clear softening toward T N appears in the elastic constants in a high magnetic field. This result suggests a breakdown of the time reversal symmetry in the temperature range between T MI and T N . Such a breakdown is considered to be due to the coupling between the dipole moment and the octupole moment, which is allowed only in T h symmetry.

On the Finite Temperature Drude Weight of the Anisotropic Heisenberg Chain

Abstract: We present a study of the Drude weight D ( T ) of the spin-1/2 X X Z chain in the gapless regime. The thermodynamic Bethe ansatz (TBA) is applied in two different ways. In the first application we employ the particle basis of magnons and their bound states. In this case we rederive and considerably extend earlier work in the literature. However, in the course of our investigation we find arguments that cast doubt on the applicability of the TBA in this case. In a second application by use of the spinon and anti-spinon particle basis we obtain completely different results. Only for anisotropy parameter Δ close to 0 we find that D ( T ) is a monotonously decaying function of temperature. For Δ close to 1 the behaviour is entirely different showing a finite temperature maximum. Also for the isotropic antiferromagnetic chain (Δ=1) the results for D ( T ) are finite for T =0 as well as for T >0 with an infinite positive slope at T =0.

Local Heavy Quasiparticle in Four-Level Kondo Model

Abstract: An impurity four-level Kondo model, in which an ion is tunneling among 4-stable points and interacting with surrounding conduction electrons, is investigated using both perturbative and numerical renormalization group methods. The results of numerical renormalization group studies show that it is possible to construct the ground state wavefunction including the excited ion states if we take into account the interaction between the conduction electrons and the ion. The resultant effective mass of quasiparticles is moderately enhanced. This result offers a good explanation for the enhanced and magnetically robust Sommerfeld coefficient observed in SmOs 4 Sb 12 , some other filled-skutterudites, and clathrate compounds.

Synchronization of Chaotic Fractional Chen System

Abstract: In this paper, chaos synchronization for Chen's system with a fractional order (or called “the fractional Chen system”) is considered. The condition for achieving synchronization of Chen's system is analyzed on the basis of the Laplace transform theory. Numerical simulations affirm the theoretical analysis, which also provides a new synchronization method for other chaotic systems with some fractional orders.

On the Auxetic Properties of 'Rotating Rectangles' with Different Connectivity

Abstract: Auxetic materials and structures exhibit the unusual property of becoming wider when stretched and thinner when compressed, ie, they have negative Poisson’s ratios In recent years, this unusual behaviour has been predicted or experimentally measured in a number of naturally-occurring and man-made materials ranging from foams where the auxetic effect arises from the particular microstructure of the foams to silicates and zeolites where the auxetic behaviour occurs at themolecular level In these auxetic systems, the negative Poisson’s ratios can be explained in terms of models based on the geometry of the system (ie, the geometry of the material’s internal structure) and the way this geometry changes as a result of applied loads (deformationmechanism) In recent years various two and three dimensional theoretical models and structures which can lead to negative Poisson’s ratio have been proposed including, two and threedimensional ‘re-entrant’ systems, models based on rigid ‘free’ molecules, chiral structures and systems made from ‘rotating rigid units’ such as squares, triangles, rectangles or tetrahdera In all of these systems, the Poisson’s ratio does not depend on scale although it can depend on the relative dimensions of certain features in the geometry In particular we have recently shown that whilst a two-dimensional system constructed from perfectly rigid squares connected together through simple hinges at the vertices of the squares will always maintain its aspect ratio when stretched or compressed [see Fig 1(a)], ie, it will exhibit constant Poisson’s ratios equal to 1 irrespective of the size of the square or direction of loading, the equivalent structure built from hinged rigid rectangles as illustrated in Fig 1(b) will exhibit in-plane Poisson’s ratios which depend on the shape of the rectangles (the ratio of the lengths of the two sides) and the relative orientation of the rectangles (ie, the angles that two adjacent rectangles make with respect to each other) This means that for such a system, the Poisson’s ratios will be strain dependent and dependent on the direction of loading This note is aimed at highlighting the fact that there exist two types of ‘rotating rectangles’ structures, and that two systems based on the same ‘building block’ (rigid rectangle) and same deformation mechanism (rectangle rotation), but different connectivity, exhibit very different mechanical properties More specifically, for rectangles of the same size (a b), tessellating corner-sharing rectangular networks in which each corner is shared between two rectangles can only be formed from two connectivity schemes, which we shall refer to as Type I and Type II The Type I network refers to the system where four rectangles are connected in such a way that the empty spaces between the rectangles form rhombi of size (a a) and (b b) as illustrated in Fig 1(b) The Type II network refers to the system with a connectivity where the empty spaces between the rectangles form parallelograms of size (a b) as illustrated in Fig 1(c) If the four rectangles are connected in any other way (for example, with the empty spaces between the rectangles forming a ‘kite’ of side lengths ‘a, a, b, b’) the resulting unit cannot form a tessellating structure The Type I ‘rotating rectangles’ structure has been extensively studied and it has been shown that this structure exhibits properties which are dependent on the shape and size of the rectangles and are strain dependent and anisotropic In particular it has been shown that such Type I ‘rotating rectangles’ structures are capable of exhibiting both positive and negative Poisson’s ratio where, for example, the on-axis Poisson’s ratios are dependent on the ratio of the lengths (a=b) and on the angle between the rectangles since: v21 1⁄4 ðv12Þ 1 1⁄4 a sin 2 ð Þ b cos 2 ð Þ a2 cos2 2 ð Þ b2 sin 2 ð Þ Here we study, for the first time, the behaviour of the Type II ‘rotating rectangles’ which as we will show exhibits very different properties As illustrated in Fig 1(c), a rectangular unit cell with cell sides are parallel to the Ox1 and Ox2 axis may be used to describe the Type II network This unit cell contains two (a b) rectangles with projections in the Oxi directions given by:

Geometrical Quadrupolar Frustration in DyB4

Abstract: Physical properties of DyB 4 have been studied by magnetization, specific heat, and ultrasonic measurements. The magnetic entropy change and ultrasonic properties in intermediate phase II indicate that the degeneracy of internal degrees of freedom is not fully lifted in spite of the formation of magnetic order. The ultrasonic attenuation and huge softening of C 44 in phase II suggest the existence of electric-quadrupolar (orbital) fluctuations of 4 f -electrons. These unusual properties originate from a geometrical quadrupolar frustration.

Revised Crystal Structure Model of Li2NH by Neutron Powder Diffraction

Abstract: We performed neutron powder diffraction experiments on lithium imide Li 2 NH, and have proposed a revised crystal structure model. Li 2 NH has a face-centred cubic structure with a partially occupi...

New A-site Ordered Perovskite Cobaltite LaBaCo2O6: Synthesis, Structure, Physical Property and Cation Order-Disorder Effect

Abstract: By means of annealing LaBaCo 2 O 5 under high pressure oxygen, we have successfully synthesized a new A-site ordered perovskite cobaltite, LaBaCo 2 O 6 . The structure and electromagnetic propertie...

Reorientation phenomenon in a magnetic phase of ε-Fe2O3 nanocrystal

Abstract: We observed an unusual magnetic phase transition in the magnetic phase of e -Fe 2 O 3 nanorods (Neel temperature = 495 K). In the cooling process at 1 kOe, the magnetization value ( M ) of the e -F...

Parametric Representation for the Multisoliton Solution of the Camassa–Holm Equation

Abstract: The parametric representation is given to the multisoliton solution of the Camassa–Holm equation. It has a simple structure expressed in terms of determinants. The proof of the solution is carried out by an elementary theory of determinants. The large time asymptotic of the solution is derived with the formula for the phase shift. The latter reveals a new feature when compared with the one for the typical soliton solutions. The peakon limit of the phase shift is also considered, showing that it reproduces the known result.

Anisotropic Superconducting Gap in Transuranium Superconductor PuRhGa5: Ga NQR Study on a Single Crystal

Abstract: 69,71 Ga NMR/NQR studies have been performed on a single crystal of the transuranium superconductor PuRhGa 5 with T c ≃9 K. We have observed a 69 Ga NQR line at ∼29.15 MHz, and assigned it to the 4 i Ga site using the NMR results. The 69 Ga NQR spin–lattice relaxation rate 1/ T 1 shows no coherence peak just below T c , but obeys T 3 behavior below T c . This result strongly suggests that PuRhGa 5 is an unconventional superconductor having an anisotropic superconducting gap. The gap amplitude 2Δ 0 ( T →0)≃5 k B T c and the residual density of states N res ( T =0)/ N 0 ( T = T c )≃0.25 have been determined assuming a simple polar function of the form Δ(θ,φ)=Δ 0 cos θ, where θ and φ are angular parameters on the Fermi surface.

Kolmogorov Spectrum of Quantum Turbulence

Abstract: There is a growing interest in the relation between classical turbulence and quantum turbulence. Classical turbulence arises from complicated dynamics of eddies in a classical fluid. In contrast, quantum turbulence consists of a tangle of stable topological defects called quantized vortices, and thus quantum turbulence provides a simpler prototype of turbulence than classical turbulence. In this paper, we investigate the dynamics and statistics of quantized vortices in quantum turbulence by numerically solving a modified Gross–Pitaevskii equation. First, to make decaying turbulence, we introduce a dissipation term that works only at scales below the healing length. Second, to obtain steady turbulence through the balance between injection and decay, we add energy injection at large scales. The energy spectrum is quantitatively consistent with the Kolmogorov law in both decaying and steady turbulence. Consequently, this is the first study that confirms the inertial range of quantum turbulence.

Origin of Weak Pseudogap Behaviors in Na0.35CoO2: Absence of Small Hole Pockets

Abstract: We analyze the normal electronic states of Na 035 CoO 2 based on the effective d – p model with a full d -orbital freedom using the fluctuation-exchange (FLEX) approximation The electronic states sensitively depend on the topology of Fermi surfaces, which changes with the crystalline electric splitting (CES) due to the trigonal deformation We succeed in reproducing the weak pseudogap behaviors in the density of states (DOS) and in the uniform magnetic susceptibility below 300 K, assuming that six small hole pockets predicted by LDA band calculations are absent If these pockets exist, on the contrary, “anti-pseudogap behaviors” should inevitably appear Thus, the present study strongly supports the absence of the small hole pockets in Na 035 CoO 2 , as reported by recent ARPES measurements A large Fermi surface around the Γ-point would account for the superconductivity in water-intercalated samples

Collision Dynamics of Two Barchan Dunes Simulated Using a Simple Model

Abstract: The collision processes of two crescentic dunes called barchans are systematically studied using a simple computer simulation model. The simulated processes, coalescence, ejection and reorganization, qualitatively correspond to those observed in a water tank experiment. Moreover we found the realized types of collision depend both on the mass ratio and on the lateral distance between barchans under initial conditions. A simple set of differential equations to describe the collision of one-dimensional (1D) dunes is introduced.

Novel pressure phase diagram of heavy fermion superconductor CePt3Si investigated by ac calorimetry

Abstract: The pressure dependences of the antiferromagnetic and superconducting transition temperatures have been investigated by ac heat capacity measurement under high pressures for the heavy-fermion superconductor CePt 3 Si without inversion symmetry in the tetragonal structure. The Neel temperature T N = 2.2 K decreases with increasing pressure and becomes zero at the critical pressure P AF ≃0.6 GPa. On the other hand, the superconducting phase exists in a wider pressure region from ambient pressure to about 1.5 GPa. The pressure phase diagram of CePt 3 Si is thus very unique and has never been reported before for other heavy fermion superconductors.

Non-generality of the Kadowaki-Woods Ratio in Correlated Oxides

Abstract: An explicit expression for the Kadowaki-Woods ratio in correlated metals is derived by invoking saturation of the (high-frequency) Fermi-liquid scattering rate at the Mott-Ioffe-Regel limit. Significant deviations observed in a number of oxides are quantitatively explained due to variations in carrier density, dimensionality, unit cell volume and the number of individual sheets in the Brillouin zone. A generic re-scaling of the original Kadowaki-Woods plot is also presented.

Magnetic Correlation of NaxCoO2 and Successive Phase Transitions of Na0:5CoO2 —NMR and Neutron Diffraction Studies—

Abstract: Data taken by various methods including NMR/NQR and neutron scattering are presented for Na x CoO 2 , particularly Na 0.5 CoO 2 . Attention has also been paid to the x dependence of the electronic nature of this system. The pseudo-gap-like behavior observed in the region of x < x c ∼0.6 is emphasized. For samples with x ≤0.6, signals from two kinds of Co sites with different quadrupole frequencies ν Q of ∼4.1 and ∼2.8 MHz were observed, and the former ν Q , which is nearly equal to that of the superconducting system Na 0.3 CoO 2 · y H 2 O, becomes dominant with decreasing x to 0.3. For Na 0.5 CoO 2 , the Co sites with the larger ν Q have larger magnetic moments. They align antiferromagnetically at T c1 ∼87 K with their direction within the plane, while the Co sites with the smaller ν Q have smaller moments. They align in the direction parallel to the c axis. The ordered moments at the two distinct sites exhibit the same T -dependence, indicating that the existence of these sites is not due to macroscopic ...

The Kondo Effect in Non-Equilibrium Quantum Dots: Perturbative Renormalization Group

Abstract: While the properties of the Kondo model in equilibrium are very well understood, much less is known for Kondo systems out of equilibrium. We study the properties of a quantum dot in the Kondo regime, when a large bias voltage V and/or a large magnetic field B is applied. Using the perturbative renormalization group generalized to stationary nonequilibrium situations, we calculate renormalized couplings, keeping their important energy dependence. We show that in a magnetic field the spin occupation of the quantum dot is non-thermal, being controlled by V and B in a complex way to be calculated by solving a quantum Boltzmann equation. We find that the well-known suppression of the Kondo effect at finite V ≫ T K (Kondo temperature) is caused by inelastic dephasing processes induced by the current through the dot. We calculate the corresponding decoherence rate, which serves to cut off the RG flow usually well inside the perturbative regime (with possible exceptions). As a consequence, the differential conduc...

Specific Heat Study on Sm-based Filled Skutterudite Phosphides SmT4P12 (T=Fe, Ru and Os)

Abstract: Sm-based filled skutterudite phosphides SmFe 4 P 12 , SmRu 4 P 12 and SmOs 4 P 12 synthesized at high temperatures and high pressures have been studied by specific heat measurements in magnetic fields. SmFe 4 P 12 shows an anomaly at 1.6 K attributed to a ferromagnetic transition. SmRu 4 P 12 shows a metal–insulator transition at 16 K. This transition consists of two successive transitions, which suggests orbital and antiferromagnetic orderings. SmOs 4 P 12 shows a sharp anomaly at 4.5 K due to an antiferromagnetic ordering. We discuss the characteristic behavior of those phase transitions and the crystalline electric field state in Sm T 4 P 12 ( T =Fe, Ru and Os). Interestingly, the magnetic entropy of SmFe 4 P 12 have only 0.16 R ln 2 below the ferromagnetic ordering temperature. This suggests a strong spin fluctuation effect. On the other hand, the variation of magnetic entropy in SmRu 4 P 12 and SmOs 4 P 12 reaches to nearly R ln 4 below the ordering temperature.

An alternative explanation for the negative Poisson's ratios in auxetic foams

Abstract: Auxetic materials exhibit the unusual property of becoming fatter when stretched and thinner when compressed, in other words they exhibit a negative Poisson’s ratio. A class of such materials which have attracted a lot of attention are auxetic foams which exhibit various enhanced physical characteristics. Foams with negative Poisson’s ratios (see Fig. 1) were first manufactured by Lakes and can be produced from commercially available conventional foams through a process involving volumetric compression, heating beyond the polymer’s softening temperature and then cooling whilst remaining under compression. Various two-dimensional models which represent a crosssection of foams have been proposed in an attempt to relate the experimentally measured values of the Poisson’s ratios to the microstructure of the foams. For example it has been proposed that conventional foams can be modelled using hexagonal and diamond-shaped honeycombs whilst the auxetic foams can be modelled through modified versions of these honeycombs. In the case of the 2D hexagonal honeycomb model, the required structural modification for auxetic behaviour requires the junctions connecting the honeycomb cell walls (‘ribs’) to be transformed during processing from ‘Y’-shaped joints to ‘arrow head’-shaped joints. For the diamond honeycomb model, auxetic behaviour requires selective removal in a regular manner of ribs during the transformation process. One should note that these two modifications need not be simultaneously applied for a foam or honeycomb to become auxetic. For example, the creation of acute angles in the hexagonal honeycombs through the conversion of the ‘Y’-shaped joints to ‘arrow head’-shaped joints is enough to make the honeycombs auxetic without the need of altering the topology of the cells by the removal of ribs. Although the above models probably play some role in modelling the auxetic behaviour in foams, and these models can reproduce the experimentally measured values of the Poisson’s ratios, one may argue that there is not enough experimental evidence to justify the assumption that either of these are the main structural modifications which result in the observed auxetic effect. For example, whilst there is experimental evidence that there are ‘broken ribs’ on the surface of the auxetic foams [see Fig. 1(b)], it is still not clear whether ‘broken ribs’ are also present in the bulk of the foam material. Also, the requirement in the diamond honeycomb model for the removal of ribs in a regular fashion is not likely to occur in the existing foam conversion process. In the case of the hexagonal models there is no clear experimental evidence that a majority of the ‘Y’ shaped joints in the conventional foam are converted to the required ‘arrow shaped’ joints during the compression/heat treatment process. In fact, one may argue that it is unlikely that the majority of the changes in the foam manufacture process are concentrated at the joints of the foam as one usually observes that the ribs of open cell foams are slightly thicker in the proximity of the joints than at the centre of the ribs. In view of this we propose a new model to explain the presence of negative Poisson’s ratios in foams. This new model is based on the hypothesis that it is more likely that changes in the microstructure during the compression/heat treatment process will conserve the geometry at the joints (i.e., they do not become re-entrant) and the topology of the system (i.e., there are no rib breakages, as was the case in the re-entrant systems) and instead, the major deformations will occur along the length of the ribs which buckle (the foam is typically subjected to ca. 30% compressive strain along each axis). Figure 1(b) provides clear evidence of the presence of buckled ribs in the transformed auxetic foam microstructure. We also assume that the additional thickness in the proximity of the joints will make it possible for the joints to behave, to a first approximation, as ‘rigid joints’. It is proposed that the rigid joints rotate relative to each other during the foam conversion process. The foam microstructure then ‘freezes’ in this much more compact form when the foam is cooled to below its softening temperature. An illustration of this is given in Fig. 2 which shows how a conventional two-dimensional hexagonal honeycomb in Fig. 2(a) (which can be treated as a two-dimensional model for conventional foams) can be converted through the compression/heat treatment process into an auxetic form shown in Fig. 2(b). We propose that the ‘rigid joints’ behave like ‘rigid triangles’ [Fig. 2(a)] which, during the heating/ compression process, rotate relative to each other to produce the more compact microstructure shown in Fig. 2(b). (This occurs though the formation of ‘kinks’ at the centre of the ribs which are the result of extensive buckling of the ribs in the compression/heat treatment process.) Uniaxial tensile loading of the idealised microstructure in Fig. 2(b) will cause a re-rotation of the triangles to generate the auxetic effect as illustrated in Fig. 2(c). (This corresponds to reFig. 1. SEM images of (a) conventional (non auxetic) open-cell polyurethane foams, and (b) auxetic open-cell polyurethane foam.